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    <title>Pinboard (cshalizi)</title>
    <link>https://pinboard.in/u:cshalizi/public/</link>
    <description>recent bookmarks from cshalizi</description>
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      <rdf:Seq>	<rdf:li rdf:resource="https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0549"/>
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  </channel><item rdf:about="https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0549">
    <title>USP: an independence test that improves on Pearson’s chi-squared and the G-test | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</title>
    <dc:date>2025-01-10T15:06:42+00:00</dc:date>
    <link>https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0549</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present the $U$-statistic permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson’s $\chi^2$-test of independence, or the $G$-test, are typically used for this task, but we argue that these tests have serious deficiencies, both in terms of their inability to control the size of the test, and their power properties. By contrast, the USP test is guaranteed to control the size of the test at the nominal level for all sample sizes, has no issues with small (or zero) cell counts, and is able to detect distributions that violate independence in only a minimal way. The test statistic is derived from a $U$-statistic estimator of a natural population measure of dependence, and we prove that this is the unique minimum variance unbiased estimator of this population quantity. The practical utility of the USP test is demonstrated on both simulated data, where its power can be dramatically greater than those of Pearson’s test, the $G$-test and Fisher’s exact test, and on real data. The USP test is implemented in the R package USP."]]></description>
<dc:subject>to:NB dependence_measures hypothesis_testing independence_testing statistics samworth.richard_j.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0861a549ae01/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dependence_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:independence_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:samworth.richard_j."/>
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<item rdf:about="https://arxiv.org/abs/1906.01850">
    <title>[1906.01850] On Testing Marginal versus Conditional Independence</title>
    <dc:date>2019-06-06T13:48:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.01850</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such models, one from each type of independence, that are closest to each other in the Kullback-Leibler sense as they approach the intersection. They become indistinguishable if the signal strength, as measured by the product of two correlation parameters, decreases faster than the standard parametric rate. Under local alternatives at such rate, we show that the asymptotic distribution of the likelihood ratio depends on where and how the local alternatives approach the intersection. To deal with this non-uniformity, we study a class of "envelope" distributions by taking pointwise suprema over asymptotic cumulative distribution functions. We show that these envelope distributions are well-behaved and lead to model selection procedures with uniform error guarantees and near-optimal power. To control the error even when the two models are indistinguishable, rather than insist on a dichotomous choice, the proposed procedure will choose either or both models."]]></description>
<dc:subject>to:NB independence_testing statistics richardson.thomas</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:243c0f221f82/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
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<item rdf:about="https://arxiv.org/abs/1804.07203">
    <title>[1804.07203] The Hardness of Conditional Independence Testing and the Generalised Covariance Measure</title>
    <dc:date>2018-05-18T01:12:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1804.07203</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["It is a common saying that testing for conditional independence, i.e., testing whether X is independent of Y, given Z, is a hard statistical problem if Z is a continuous random variable. In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Statistical tests are required to have a size that is smaller than a predefined significance level, and different tests usually have power against a different class of alternatives. We prove that a valid test for conditional independence does not have power against any alternative. 
"Given the non-existence of a uniformly valid conditional independence test, we argue that tests must be designed so their suitability for a particular problem setting may be judged easily. To address this need, we propose in the case where X and Y are univariate to nonlinearly regress X on Z, and Y on Z and then compute a test statistic based on the sample covariance between the residuals, which we call the generalised covariance measure (GCM). We prove that validity of this form of test relies almost entirely on the weak requirement that the regression procedures are able to estimate the conditional means X given Z, and Y given Z, at a slow rate. We extend the methodology to handle settings where X and Y may be multivariate or even high-dimensional. 
"While our general procedure can be tailored to the setting at hand by combining it with any regression technique, we develop the theoretical guarantees for kernel ridge regression. A simulation study shows that the test based on GCM is competitive with state of the art conditional independence tests. Code will be available as an R package."]]></description>
<dc:subject>to:NB independence_testing hypothesis_testing statistics causal_discovery heard_the_talk to_read peters.jonas nonparametrics have_skimmed</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:06e5ea6a376c/</dc:identifier>
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